Morne Morkel (2/30) and Umesh Yadav (2/18) bowled a tight line to help Kolkata restrict Delhi to 146 for 8 and Gambhir heaped praise on his bowlers, especially Umesh Yadav.
"A lot of credit needs to go to the bowlers, especially Umesh, he's been unbelievable, especially that last over he bowled," he said after defending champions Kolkata overhauled the 147-run target in 18.1 overs.
"It's a luxury to have Morne, Umesh and Sunil in the same team. All that matters for KKR is how many points we have. It doesn't matter how many runs I get," he added.
Adjudged man-of-the-match, Umesh Yadav, who was part of the Indian World Cup team, said he tried to bowl yorkers in the death overs.
"I'm just focussing on my line and length, that's it. I had a lot of confidence from the World Cup. I just wanted to use the pace and skiddy bounce on this wicket," he said.
"If I'm bowling length in the last overs it's very easy to hit sixes, that's why I was bowling the yorkers," he added.
Put into bat, Delhi failed to put up a big partnership and skipper JP Duminy said losing wickets at regular intervals put paid to their chances.
"We had a pretty dreadful start, losing as many wickets as we did. I still thought 146 was defendable on this wicket, but we didn't put the ball on a good spot consecutively enough," he said.
"We'll eventually get there. We know we were well below par today, but there's a long way to go in the tournament, and I'm looking forward to the challenge," he said.